Here's a brief story. Shiva was once in deep meditation. While he was meditating, his wife Parvati playfully covered his eyes. As a result, the world plunged into darkness for a while. This story shows the close relationship between Shiva and Parvati and how their actions can have an impact on the world.
One story is about Shiva and his bull Nandi. Nandi is Shiva's vehicle. The story goes that Nandi is always by Shiva's side, showing loyalty. Shiva is often depicted with Nandi, and it represents Shiva's connection with nature and the animal kingdom.
Sure. There's the story of Shiva's battle with the demon Andhaka. Andhaka was very powerful and had many heads. Shiva fought him valiantly and finally killed him. This shows Shiva's power as a protector.